## Saturday, November 26, 2011 ... /////

### Andrea Rossi: pressure and boiling point

No boiling occurs in the "reactor"; numbers match

In June, Swedish server Cornucopia looked at the following 13-minute June 2011 presentation by Andrea Rossi organized for Steven Krivit, a critic of Rossi's cold fusion whose negative attitude could however be just a part of Rossi's theater, a little bit critically and with some updates from TRF, it becomes pretty hilarious. The explanation should be comprehensible to everyone who's been exposed at least to high school physics.

Rossi's comments are so naive that it actually seems plausible to me that he is not realizing the simple mistake. Alternatively, he knows very well what he's doing, trying to earn some money by fraud. Andrea Rossi has claimed that a secret consumer has ordered the devices for $24 million. One may buy lots of chewing gums for that, or whatever you prefer. ;-) The "reactor" needs some energy from the grid. This point itself is rather bizarre: if it were a real reactor, why would it need any inflow of energy at all? Rossi doesn't offer any answer but he claims that the "reactor" produces much more energy than what it consumes which would still be enough to prove the existence of a new source of energy. And that's why some people unfamiliar with nuclear physics behind fusion are excited. But is it the case? He is taking 3.4 Amperes at 220 Volts ie. 748 Joules per second (or 2.7 MJ per hour: we multiplied by 3,600) from the grid. Every hour, he claims to convert 7 kilograms of water (from 26.5 °C) to steam (at 100.1 °C). How much energy do you need to heat up (and, perhaps, evaporate) the water each hour? Well, 7 kilograms (per hour) times 4,200 Joules per kilogram and per Celsius degree times (100-26.5) °C is 2.17 MJ per hour, nicely and perfectly below 2.7 MJ taken from the grid. You could call it a perfect agreement, a relatively high 80% efficiency in converting the electricity to heat. ;-) Things are just perfectly fine as long as you accept that Mr Rossi isn't actually evaporating (almost) any water at all so only the heat capacity, and not the latent heat, should be counted. (If you believed that the water evaporates, you would need 18 MJ per hour in total because you have to add the latent heat 7 kilogram times 2.23 MJ per kilogram. That would be a contradiction.) With some help from the Swedish server and an extra refined argument from your humble correspondent, you may easily see that the bulk of the water can't be evaporating in the "reactor". Why? It's easy. The main argument Mr Rossi offers that the water is evaporating in the "reactor" is that the temperature at some point of the "reactor" is 100.1 °C. Rossi says that the "everyone knows" that this temperature is above the boiling point. Well, it actually isn't. Let's start slowly. The figure is dangerously close to the boiling point and you should be careful whether it's above the real boiling point or not. Well, one may easily prove that it's not above the boiling point in the conditions of the experiment. This is the graph I found that shows the dependence of the boiling point of water on the external pressure. The slope near 100 °C is about 2 times steeper than the slope of the proportionality curve going through the same point (1 atmosphere, 100 °C) as well as the origin (0 Pascal, 0 °C). So 100.1 °C which is 0.1 percent above 100 °C corresponds to the external pressure that is about 0.2 percent greater than 1 atmosphere. So the pressure has to exceed one atmosphere or 101,325 Pa by more than 200 Pa and the boiling point is already above 100.1 °C. First of all, it was a hot day so the temperature in the room was above 30 °C as he said. Chances are that the pressure in Italy was above 101,325+200 Pa as well. The atmospheric pressure in Italy is usually above 102 kPa which means that the boiling point of water in Italy is usually above 100.5 °C. Rossi doesn't give us any information about the precise pressure. If you rely on the claim that your temperature 100.1 °C is above the boiling point, you surely need to know the air pressure in the room with the same precision. It also helps that the elevation of Bologna is just 50 meters above the sea level. It only reduces the pressure, relatively to the sea level, by $h\rho g = 500$ Pascal or so, so if you start with 102,500 (re-normalized for the sea level) like the current pressure in Venice above, you still remain well above 101,325 Pa and the boiling point is still well above 100 °C, by several tenths of a degree if not a whole degree. By the way, Wolfram Alpha is a powerful tool. The pressure in Bologna on June 20th, 2011 (when the video was recorded or at least posted) around the noon was 101,600 Pa or so, i.e. 1.003 atmospheres, so the boiling point was about 100.15 °C: so his temperature was beneath the boiling point of water even at zero hydrostatic pressure (see below). Second of all, and this is also my addition to the Swedish argument, there are extra corrections to the pressure coming from Bernoulli's equation $\frac{v^2}{2} + gz + \frac{p}{\rho} = {\rm constant}$ The speed of the water in the rubber is so small that the first term is negligible. However, there's also the second term, the potential energy of water. How big is it? Well, if we want to raise the boiling point by those 0.1 °C, we need the pressure to be higher by 200 Pa or so, as we have said. So the $p/\rho$ term is about $200/1,000$ = 0.2 Joules per kilogram. That is equal to the $gz$ potential term for $z=2$ centimeters because $g=10$ or so. Just to be sure, the pressure is higher when you're "deeper" in water. So 2 centimeters of water column above you is enough to guarantee that the water's boiling point in the depth is elevated by 0.1 °C. It's not hard to optically see that the "chimney" described by Rossi is taller than 2 centimeters so it is almost certainly enough to increase the pressure of water sufficiently for the boiling point at the bottom to be above 100.1 °C. When Rossi says that the pressure inside the "reactor" is exactly the atmospheric pressure, it's really a misleading, inconsistent statement. The pressure inside water depends on the depth in the water (at some depths, his "universal" statement about the room pressure is inevitably wrong) so at a higher depth, the pressure is necessarily higher as well. Only centimeters are needed to correct the boiling point by 0.1 °C. Some extra pressure may be there because the outgoing tube is thin enough (somewhere in the middle) and prevents the (small amount of) steam to get out quickly. In the fast comments, Honza mentions that a slight contamination of the water by something like salt may change the boiling point, too. Properties of the phases of water depend on the temperature and pressure in various ways, like seen in this funny trick with an easy vaporization of almost boiling water in a freezing (!) weather. So what goes out from the tube isn't really "pure steam" with some "little condensation" as Rossi puts it. (He also tries to explain away the almost invisible steam arguably coming from 2 milliliters per second by saying that this "hot" steam at 100.1 °C is almost transparent. That's just a bogus argument – because any steam will ultimately cool down once it interacts with the cooler air – suggesting that he is intentionally deceiving the viewers. Be sure that 2 milliliters of water converted to steam each second would be both more visible and they would create a "bigger wind" and much louder "sizzling" and "hissing" than what he is showing: it should be over 3 liters of steam per second, because its density is 0.6 kg per cubic meter, a lot of gas, indeed. With such a thin tube, the speed of the outgoing steam should be many meters per second and it's apparently not.) It's a warm sub-boiling-point water dropping at 7 liters per hour e.g. 2 milliliters per second, with a small mixture of steam. Some of this warm water evaporates; most of the evaporated water spontaneously evaporates outside the "reactor". Aside from the arguments above showing that the pressure in the "reactor" was almost certainly high enough for the boiling point to be above 100.1 °C, one could also argue that the pressure wasn't ever adjusted for the sea level to remain "inside the reactor" and the boiling at 100.1 °C simply isn't fast enough to produce 2 milliliters of steam per second in such a small "reactor". If there were some genuine "fusion" going on, the temperature of the nickel or metallic component would almost certainly be above 100 °C so there would also be no reason to expect the steam to be "right above" the boiling point. It could be 110 or 150 or 200 °C. A temperature very close to 100 °C only suggests one thing: that he raised the temperature enough to make his viewers think that the water had to boil even though it didn't. Summary So what Andrea Rossi has achieved was to use the electricity from the power outlet to heat the water right beneath the boiling point at a 80 percent efficiency; something that a good housewife should be able to do in the kitchen at least twice a day (and some of the housewives are even capable of making the water boil). If Mr Rossi has a genuine reactor, a simple way to disprove this description of the details of his stupidity (or his naive magic) is to heat the water/steam to 110 °C instead of 100.1 °C using the same gadget. ;-) This is not too much to ask for: typical steam generators in nuclear power plants are pressurized at 60-160 atmospheres and the temperature of water and steam is 220-315 °C. Meanwhile, if an American consumer really paid$24 million for this ugly electric coffee machine, I recommend him to eat his feces for the dinner, too. He may send me \$20 million (discount!) for the great know-how. It will be an equally intelligent investment and an equally progressive consumption of an equally revolutionary food product.

And that's the memo.

The phase diagram of water. Pressure is on the x-axis, temperature on the y-axis. Aside from steam, water, and ice "one", there are six other exotic types of ice at high pressures and low temperatures.

P.S.: By the way, there are of course many more sophisticated ways how the visual impressions from the video could have been achieved. A wireless transfer of energy; using burning of some external hydrogen pumped into the "reactor" to get the steam and heat, and so on.

But my impression is that Rossi is the most simple-minded kind of a countryside "genius" who wouldn't be motivated or capable of doing any of these fancy things. So the confusion his famous "invention" is all about depends on the inability of the people to distinguish water and steam in a tube (which subsequently boils down or, more precisely, fails to boil down because of naive ideas about the boiling point and the constancy of pressure), whether or not this "trick" is deliberate or whether Rossi is among his own victims; whether or not his naive manipulations with the "constant" boiling point and the constant universal pressure are intentional tricks to mislead the viewers or results of his authentic and honest intellectual limits.